There have been some changes to Mac USB-C ports … the ones on Apple Silicon Macs support USB4, and some of them support Thunderbolt 4. That shouldn't matter as far as connecting an iPhone to a Mac, where the connection would involve USB 2 or USB 3.
The Technical Specifications for the iPhone 16 Pro say
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Syncing to a Mac or PC requires:
- macOS Catalina 10.15 or later using the Finder
- macOS High Sierra 10.13 through macOS Mojave 10.14.6 using iTunes 12.8 or later
- Windows 10 or later using iTunes 12.12.10 or later
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If your 2017 iMac was still running its original OS (Sierra), it would not meet these requirements. But your tag line says that you are running macOS 13.7 (Ventura), so you should be OK there.
There are "charging only" cables that don't carry data at all … and if you used one of them, that would explain the symptoms. But you say that you used the same cable successfully with a M1 MacBook Air.
You may want to check Finder > Settings… on the iMac. I'm guessing that in the Sidebar tab, you want to have a check mark next to "CDs, DVDs, and iOS Devices" (under the Locations heading).
If this does not resolve the issue, you may want to take advantage of the 90 days of free telephone support which came with your new iPhone 16 Pro.